Solve for $x$ and $y$ using elimination. ${-2x+y = -12}$ ${-3x-y = -33}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-5x = -45$ $\dfrac{-5x}{{-5}} = \dfrac{-45}{{-5}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-2x+y = -12}\thinspace$ to find $y$ ${-2}{(9)}{ + y = -12}$ $-18+y = -12$ $-18{+18} + y = -12{+18}$ ${y = 6}$ You can also plug ${x = 9}$ into $\thinspace {-3x-y = -33}\thinspace$ and get the same answer for $y$ : ${-3}{(9)}{ - y = -33}$ ${y = 6}$